RoboguruRoboguru
SD

Tentukan nilai mutlak dari ∣∣​2n−n+11​∣∣​, n bilangan asli

Pertanyaan

Tentukan nilai mutlak dari open vertical bar 2 n minus fraction numerator 1 over denominator n plus 1 end fraction close vertical bar comma space n space bilangan space aslispace space 

R. Utami

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai mutlak dari open vertical bar 2 n minus fraction numerator 1 over denominator n plus 1 end fraction close vertical bar comma space n space bilangan space asli adalah fraction numerator 2 n squared plus 2 n minus 1 over denominator n plus 1 end fraction comma space dengan space n space bilangan space asli.space space 

Pembahasan

Ingat,

Definisi nilai mutlak

open vertical bar a close vertical bar equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row a cell jika space a greater or equal than 0 end cell row cell negative a end cell cell jika space a less than 0 end cell end table close

Himpunan bilangan asli

open curly brackets 1 comma 2 comma 3 comma 4 comma 5 comma........... close curly brackets

Pengurangan pecahan

Diperoleh sebagai berikut

open vertical bar 2 n minus fraction numerator 1 over denominator n plus 1 end fraction close vertical bar comma space n space bilangan space asli

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 n minus fraction numerator 1 over denominator n plus 1 end fraction close vertical bar end cell equals cell open vertical bar fraction numerator 2 n open parentheses n plus 1 close parentheses over denominator n plus 1 end fraction minus fraction numerator 1 over denominator n plus 1 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator 2 n squared plus 2 n minus 1 over denominator n plus 1 end fraction close vertical bar end cell end table

Karena n bilangan asli, sehingga n bernilai positif akibatnya 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 n squared plus 2 n minus 1 over denominator n plus 1 end fraction end cell greater or equal than 0 end table

Sesuai definisi nilai mutlak, maka

open vertical bar 2 n minus fraction numerator 1 over denominator n plus 1 end fraction close vertical bar equals open vertical bar fraction numerator 2 n squared plus 2 n minus 1 over denominator n plus 1 end fraction close vertical bar equals fraction numerator 2 n squared plus 2 n minus 1 over denominator n plus 1 end fraction

Dengan demikian nilai mutlak dari open vertical bar 2 n minus fraction numerator 1 over denominator n plus 1 end fraction close vertical bar comma space n space bilangan space asli adalah fraction numerator 2 n squared plus 2 n minus 1 over denominator n plus 1 end fraction comma space dengan space n space bilangan space asli.space space 

41

0.0 (0 rating)

Pertanyaan serupa

Tentukan nilai mutlak dari ∣∣​(3n)2n−1∣∣​, n bilangan asli

37

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia